The turbine shrouds surrounding turbine rotors are normally segmented in the circumferential direction to allow for thermal expansion. Being exposed to very hot combustion gasses, the turbine shrouds usually need to be cooled. Since flowing coolant through a shroud assembly diminishes overall engine efficiency, it is desirable to minimize cooling flow consumption without degrading shroud segment durability. Individual feather seals are typically installed in confronting slots defined in the end walls of circumferentially adjacent turbine shroud segments to prevent undesirable cooling flow leakage at the inter-segment gaps between adjacent shroud segments. While such feather seal arrangements generally provide adequate inter-segment sealing, there is a continued need for alternative sealing and cooling shroud arrangements.